Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.

https://link.springer.com/content/pdf/10.3758/BRM.40.3.879.pdf

Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models

This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

/pdf/addressing-moderated-mediation-hypotheses-theory-methods-and-463wvvjm24.pdf

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions.

The purpose of this paper is to provide a comprehensive, yet concise, overview of the considerations and metrics required for partial least squares structural equation modeling (PLS-SEM) analysis and result reporting. Preliminary considerations are summarized first, including reasons for choosing PLS-SEM, recommended sample size in selected contexts, distributional assumptions, use of secondary data, statistical power and the need for goodness-of-fit testing. Next, the metrics as well as the rules of thumb that should be applied to assess the PLS-SEM results are covered. Besides presenting established PLS-SEM evaluation criteria, the overview includes the following new guidelines: PLSpredict (i.e., a novel approach for assessing a model’s out-of-sample prediction), metrics for model comparisons, and several complementary methods for checking the results’ robustness.,This paper provides an overview of previously and recently proposed metrics as well as rules of thumb for evaluating the research results based on the application of PLS-SEM.,Most of the previously applied metrics for evaluating PLS-SEM results are still relevant. Nevertheless, scholars need to be knowledgeable about recently proposed metrics (e.g. model comparison criteria) and methods (e.g. endogeneity assessment, latent class analysis and PLSpredict), and when and how to apply them to extend their analyses.,Methodological developments associated with PLS-SEM are rapidly emerging. The metrics reported in this paper are useful for current applications, but must always be up to date with the latest developments in the PLS-SEM method.,In light of more recent research and methodological developments in the PLS-SEM domain, guidelines for the method’s use need to be continuously extended and updated. This paper is the most current and comprehensive summary of the PLS-SEM method and the metrics applied to assess its solutions.

https://www.emerald.com/insight/content/doi/10.1108/EBR-11-2018-0203/full/pdf

When to use and how to report the results of PLS-SEM

This is a review of bootstrap methods, concentrating on basic ideas and applications rather than theoretical considerations. It begins with an exposition of the bootstrap estimate of standard error for one-sample situations. Several examples, some involving quite complicated statistical procedures, are given. The bootstrap is then extended to other measures of statistical accuracy such as bias and prediction error, and to complicated data structures such as time series, censored data, and regression models. Several more examples are presented illustrating these ideas. The last third of the paper deals mainly with bootstrap confidence intervals.

/pdf/bootstrap-methods-for-standard-errors-confidence-intervals-9ly087s1u7.pdf

Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy

Bootstrapping is a common method for assessing confidence in phylogenetic anal? yses. Although bootstrapping was first applied in phylogenetics to assess the repeatability of a given result, bootstrap results are commonly interpreted as a measure of the probability that a phylogenetic estimate represents the true phylogeny. Here we use computer simulations and a laboratory-generated phylogeny to test bootstrapping results of parsimony analyses, both as measures of repeatability (i.e., the probability of repeating a result given a new sample of characters) and accuracy (i.e., the probability that a result represents the true phylogeny). Our results indicate that any given bootstrap proportion provides an unbiased but highly imprecise measure of repeatability, unless the actual probability of replicating the relevant result is nearly one. The imprecision of the estimate is great enough to render the estimate virtually useless as a measure of repeatability. Under conditions thought to be typical of most phylogenetic analyses, however, bootstrap proportions in majority-rule consensus trees provide biased but highly con? servative estimates of the probability of correctly inferring the corresponding clades. Specifically, under conditions of equal rates of change, symmetric phylogenies, and internodal change of 70% usually correspond to a probability of >95% that the corresponding dade is real. However, under conditions of very high rates of internodal change (approaching randomization of the characters among taxa) or highly unequal rates of change among taxa, bootstrap proportions >50% are overestimates of accuracy. (Boot? strapping; accuracy; repeatability; phylogeny; parsimony; precision; statistical analyses; simu? lations.)

An Empirical Test of Bootstrapping as a Method for Assessing Confidence in Phylogenetic Analysis

We consider the problem of setting approximate confidence intervals for a single parameter 0 in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, 8 2 &z(=), can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application, at the price of a considerable increase in computational effort. The new intervals incorporate an improvement over previously suggested methods, which results in second-order correctness in a wide variety of problems. In addition to parametric families, bootstrap intervals are also developed for nonparametric situations.

Bradley Efron

Papers

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